We model the binding energies of rovibrational levels of the RbYb molecule using experimental data from two-color photoassociation spectroscopy in mixtures of ultracold Rb-87 with various Yb isotopes. The model uses a theoretical potential based on state-of-the-art ab initio potentials, further improved by least-squares fitting to the experimental data. We have fixed the number of bound states supported by the potential curve, so that the model is mass scaled, that is, it accurately describes the bound-state energies for all measured isotopic combinations. Such a model enables an accurate prediction of the s-wave scattering lengths of all isotopic combinations of the RbYb system. The reduced mass range is broad enough to cover the full scattering lengths range from -infinity to +infinity. For example, the (RbYb)-Rb-87-Yb-174 system is characterized by a large positive scattering length of +880(120) a.u., while (RbYb)-Rb-87-Yb-173 has a = -626(88) a.u. On the other hand (RbYb)-Rb-87-Yb-170 has a very small scattering length of -11.5(2.5) a.u. confirmed by the pair s extremely low thermalization rate. For isotopic combinations including Rb-85 the variation of the interspecies scattering lengths is much smoother ranging from +39.0(1.6) a.u. for (RbYb)-Rb-85-Yb-176 to +230(12) a.u. in the case of (RbYb)-Rb-85-Yb-168. Hyperfine corrections to these scattering lengths are also given. We further complement the fitted potential with interaction parameters calculated from alternative methods. The recommended value of the van der Waals coefficient is C-6 = 2837(13) a.u. agrees with but is more precise than the current state-of-the-art theoretical predictions [M. S. Safronova, S. G. Porsev, and C. W. Clark, Phys. Rev. Lett. 109, 230802 (2012)].